Get the answer to "How do I solve this equation? 22w−3=w−23w−7"

High School
Algebra
Algebra I
Exponents and radicals

Reggie

Answered question

2021-05-16

How do I solve this equation?

\frac{2}{2 w - 3} = \frac{w - 2}{3 w - 7}

Answer & Explanation

Derrick

Skilled2021-05-17Added 94 answers

Let's start by multiplying both sides by (2w−3)(3w−7) so that we can get rid of the fractions.
2(3w−7)=(w−2)(2w−3)
6w−14=2ww−3w−4w+6
2ww−3w−10w+20=0
Now let w=x+iy. Then this becomes

2 (x^{2} + y^{2}) - 3 (x - i y) - 10 (x + i y) + 20 = 0

[2 (x^{2} + y^{2}) - 3 x - 10 x + 20] + i [3 y - 10 y] = 0

Now we can split this up into its real and imaginary parts. First let's solve the imaginary part because that looks easy:
3y−10y=0
−7y=0
y=0
Substituting that into the real part, we can then solve for x.

2 (x^{2} + 0^{2}) - 3 x - 10 x + 20 = 0

2 x^{2} - 13 x + 20 = 0

x = \frac{13 \pm ({\sqrt{13}}^{2} - 4 (2) (20))}{2} (2)

x = \frac{13 \pm 3}{4}

So the two solutions are w=4 and

w = \frac{5}{2}

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